New results of almost periodic solutions for recurrent neural networks

In this paper recurrent neural networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and local exponential stability of the almost periodic solutions are established, which are new and complement previously known results.     

Almost periodic solutions for shunting inhibitory cellular neural networks without global Lipschitz activation functions

In this paper the shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, sufficient conditions for the existence and local exponential stability of the almost periodic solutions are established by using a fixed point theorem, Lyapunov functional method and differential inequality techniques. The results of this paper are new and they complement previously known results.     

Existence and stability of positive almost periodic solutions and periodic solutions for a logarithmic population model

By means of the Cauchy matrix, we give sufficient conditions for the existence and exponential stability of almost periodic solutions and periodic solutions for the delay impulsive logarithmic population.     

The existence and uniqueness of periodic solutions for a kind of Duffing-type equation with two deviating arguments

By applying Mawhin’s continuation theorem and establishing new lemmas, some sufficient conditions for the existence and uniqueness of periodic solutions were obtained for a Duffing-type equation with two deviating arguments. Moreover, an example is given to illustrate the results.     

Interval criteria for oscillation of nonlinear second-order dynamic equations on time scales

Interval oscillation criteria are established for a second-order nonlinear dynamic equation on time scales by utilizing a generalized Riccati technique and an integral averaging technique. The theory can be applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives.     

Positive almost periodic solution for a class of Nicholson’s blowflies model with multiple time-varying delays

In this paper, we study the existence and exponential convergence of positive almost periodic solutions for the generalized Nicholson’s blowflies model with multiple time-varying delays. Under proper conditions, we establish some criteria to ensure that the solutions of this model converge locally exponentially to a positive almost periodic solution. Moreover, we give some examples to illustrate our main results.     

Oscillations and limit cycles in Lotka-Volterra systems with delays

In this paper, competitive Lotka-Volterra systems are studied that have distributed delays and constant coefficients on interaction terms and have time dependent growth rate vectors with an asymptotically constant average. Algebraic conditions are found to rule out non-vanishing oscillations for such systems and heteroclinic limit cycles for autonomous systems. As a supplement to these results, simple sufficient conditions are provided for certain components of all solutions to vanish and a criterion is given for partial permanence. An outstanding feature of all these results is that the conditions are irrelevant of the size and distribution of the delays.     

Existence of positive periodic solutions for a neutral population model with delays and impulse

In this paper, by using the theory of abstract continuous theorem of k$k$-set contractive operator and some analysis techniques, we obtain some sufficient conditions for the existence of positive periodic solutions for a neutral population model with delays and impulse.     

Reversible periodic orbits in a class of 3D continuous piecewise linear systems of differential equations

The so-called noose bifurcation is an interesting structure of reversible periodic orbits that was numerically detected by Kent and Elgin in the well-known Michelson system. In this work we perform an analysis of the periodic behavior of a piecewise version of the Michelson system where this bifurcation also exists. This variant is a one-parameter three-dimensional piecewise linear continuous system with two zones separated by a plane and it is also a representative of a wide class of reversible divergence-free systems.     

Periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay

The existence of periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay is obtained by using stability properties of a bounded solution.     

On the regularity of discrete linear systems

In this paper we have introduced a new regularity coefficient of time varying discrete linear system. On the base of this coefficient we have characterized the regularity of homogeneous discrete time varying linear systems by nonhomogeneous ones. Moreover we provided bounds for the regularity coefficient in terms of the existing in the literature regularity coefficients.     

Existence and uniqueness of periodic solutions for a class of generalized Liénard systems with forcing term

By using topological degree theory and some analysis skills, we obtain some sufficient conditions for the existence and uniqueness of periodic solutions for a class of forced generalized Liénard systems.     

Periodic solutions for dynamic equations on time scales

Massera type criteria are established for the existence of periodic solutions of linear and nonlinear dynamic equations on time scales. Some interesting properties of the exponential function on time scales are presented. Furthermore, a sufficient condition guaranteeing the boundedness of the solutions of the equation is presented.     

On superquadratic periodic systems with indefinite linear part

We consider a second order periodic system with an indefinite linear part and a potential function which is superquadratic but does not satisfy the AR-condition. Using Morse critical groups, we show that the system has at least one nontrivial solution.     

Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II

In this paper we continue the research started in a previous paper, where we proved that the linear differential equation

(1)     

Multiplicity of periodic solutions for second-order discrete Hamiltonian systems with a small forcing term

Some sufficient conditions for the existence of three periodic solutions are obtained for the second-order discrete Hamiltonian systems with a small forcing term by using a three-critical-point theorem.     

Global attractivity of positive periodic solution to periodic Lotka-Volterra competition systems with pure delay

We consider a periodic Lotka-Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems)

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Global attractivity of the almost periodic solution of a delay logistic population model with impulses

In this paper, we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations. By using a comparison theorem and constructing a suitable Lyapunov functional, a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained. As applications, some special models are studied; our new results improve and generalize former results.